1. Field of the Invention
The present invention concerns a method and a device for radial data acquisition in three-dimensional k-space in an MR measurement for a magnetic resonance system. Moreover, the present invention concerns a magnetic resonance system with the device described above.
2. Description of the Prior Art
In recent years radial three-dimensional data acquisition in k-space has become popular in the field of magnetic resonance tomography for a number of reasons. First, the data acquisition is very robust with regard to a movement (for example the movement of a patient in an MR examination) since, in the prevalent radial three-dimensional methods, each readout process (process in which multiple points of k-space are detected in one step) proceeds through the center of k-space. Moreover, radial three-dimensional data acquisition very simply enables a radial sub-sampling, so the sampling density (detected points per volume unit) is relatively low at the edges of k-space while it is relatively high in the environment of the center and in the center itself.
However, the radial three-dimensional data acquisition has the following two problem areas:
1. It is difficult to achieve an optimally uniform distribution of the data points detected in k-space.
2. Most methods for radial three-dimensional data acquisition have an interleaved procedure in which k-space is sampled repeatedly by detection steps. K-space of each detection step is thereby sampled coarsely, with every detection step essentially sampling or detecting different points of k-space than the respective other detection steps. Radial three-dimensional data acquisition of k-space is thereby composed of the results of all interleaved detection steps. The problem with this interleaved procedure is to select the order in which the points of k-space are acquired for one of the detection steps, such that this is accompanied by an optimally uniform gradient change of the magnetic field in order to minimize the eddy current effects caused by magnetic field changes.
According to a widely accepted approach to radial data acquisition in three-dimensional k-space, the data acquisition is composed of multiple readout processes, and wherein points along a spoke (i.e. a straight line segment) are detected per readout process, wherein this spoke is defined by a point on a sphere and the center point of this sphere. In other words, each spoke on which the points in k-space are detected by the corresponding readout process runs through this center point (which is located in the center of k-space) and through the corresponding point on the sphere. A spoke is thus differentiated from the other spokes by the corresponding point on the sphere since each spoke runs through the center point.
The points on the sphere (which respectively each define one of the spokes) lie on a trajectory which possesses the shape of a three-dimensional Archimedean spiral. The more points in k-space that are sampled, the more spokes exist and the more windings that the Archimedean spiral on the sphere has, so the separation of adjacent windings of the Archimedean spiral is reduced. In an interleaved procedure, for each acquisition step only every m-th spoke is sampled (when m corresponds to the number of acquisition steps). In other words—for example for the first acquisition step—the points on the spokes 1, (m+1), (2*m+1), (3*m+1) etc. are acquired while the points on the spokes k, (m+k), (2*m+k), (3*m+k) etc. are acquired for the k-th acquisition step (k≦m).
In this procedure a significant interleaving, i.e. m>>1, leads to a large gradient change of the magnetic field at the transition from one spoke to the next, which disadvantageously leads to artifacts which occur due to the effects of the eddy current.
For a radial data acquisition in three-dimensional k-space wherein the data are acquired by means of 1600 spokes, the points 1 defining these spokes are shown on a sphere 4 in FIGS. 1a, 1b and 1c. FIG. 1a shows the sphere 4 from above and FIG. 1b shows the sphere 4 at an angle from above. The depicted points 1 lie on a three-dimensional Archimedean spiral which forms the trajectory by means of which the order in which the individual spokes are processed is determined.
FIG. 1c depicts the trajectory 15 for one of these acquisition steps for the case that the entire data acquisition consists of 20 acquisition steps. The straight line segments thereby represent the transition from one spoke to the next. Since these straight line segments are relatively large at least in part, this leads to a relatively large variation in the gradient of the magnetic field that is necessary for data acquisition, which in turn induces strong eddy currents, which ultimately leads to artifacts in the imaging depending on the data acquisition.
However, the approach described above for radial data acquisition in three-dimensional k-space has the advantage of an extremely uniform sampling, so a compensation of the sampling density is significantly facilitated. The compensation of the sampling density is understood as the process in which the different sampling density (high in the center and low at the edge of k-space)—as noted above—for the imaging is compensated, such that the density of the image points (pixels) (determined from the acquired data) in the entire sampled volume is optimally uniform.
An additional approach to radial data acquisition in three-dimensional k-space is described in “Temporal Stability of Adaptive 3D Radial MRI Using Multidimensional Golden Means”, R. W. Chan et al., Magnetic Resonance in Medicine 61, Pages 354-363, 2009. The proposed method executes (at least in a time period) a uniform sampling of a two-dimensional normalized space, so the concept of the golden segment is used together with a modified Fibonacci series in order to distribute the points 1 on a sphere 4, wherein these points 1 respectively define a spoke for radial data acquisition. This sampling pattern is transferred to a spherical surface by the coordinates of the planar sampling points being coupled with the polar angle and the azimuthal angle within the three-dimensional space. The result of such a pattern is shown in FIG. 2a as a view of the sphere 4 from above and in FIG. 2b as a view of the sphere at an angle from above.
This approach is aimed at an optimally uniform sampling in the time curve. Nevertheless, with a Voronoi analysis the result is reached that the sampling distribution is not particularly uniform within a time frame. This approach consequently requires a complicated compensation of the sampling density. Ultimately, exposures are not optimally avoided with this approach.
In summary it is to be noted that the approaches to radial data acquisition in three-dimensional k-space according to the prior art are optimized either with regard to a uniform sampling density (spatial or temporal) or with regard to a suitable compensation of eddy currents (with regard to avoiding eddy currents that are too large). In most cases a complicated compensation of the sampling density is required.